So in this module, we're gonna focus on Terrain Analysis.
And the way that we do this is using some sort of digital terrain model.
Now this can either be a raster model, a DEM, a digital elevation model is what we
call those, or a TIN, a vector-based model that's triangulated irregular network.
Now we're first gonna discuss a little about the DEM or
the raster-based digital elevation or digital terrain model.
Because these are the more commonly used and they're a little bit easier
to conceptualize how they're doing the different types of analysis.
So essentially, in one of these DEMs, each cell in the raster has a single
value that represents the average elevation of that area in the real world.
So this makes it that so they're quite easy to use.
It's simply another prospect of matrix algebra to do any analysis on them.
And they're relatively easy to visualize what's happening.
They look something like this.
There are usually a couple of different color ramps for
them that we'll discuss a little bit in the demonstration for this module.
But they either sort of scale from blue to red or from blue to white.
Now if we wanna think about the values that are within there,
it is again some sort of matrix of numbers where you have certain values to represent
the average elevation for each cell, for each pixel of the DEM.
In contrast, we also have this vector-based format, the TIN,
triangulated irregular network, terrain model, where we have essentially
triangles that are drawn between a series of points that have elevations.
So it actually begins to represent the elevation in kind of a built-up triangular
way, Now when we talk about a DTM, or a digital terrain model,
this is kind of a general term referring to either one of those.
But there are a few different ways we can create these types of data,
either a digital elevation model or a TIN.
And I'm gonna go over each one of these in a little bit of detail because they're
slightly different in how we deal with these.
But first, I wanna talk a little bit about the ways that we can
use these in different analytical techniques.
In the example that I'm gonna give here is a terrain model from someplace that
that is rather striking in its terrain, and that's Crater Lake in Oregon.
There's just a few pictures of it here.
So this is an elevation model of Crater Lake.
This is a DEM, the raster-based model.
And you can see how it could have been created, or
sort of looks like a topographic map, as well.
But what we're seeing is it's scaled from low values in black
to high values in white.
So you can see the sort of caldera of Crater Lake comes up very high elevation
and then drops down into the lake itself with lower elevations.
Now, one of the uses of this type of model, this DEM model,
well, we can determine a lot of different characteristics of the terrain.
We're gonna focus on a few of these.
In addition to just being able to find out what the average elevation is at any
point across the image that we have.
We can also do things like create the slope, a measure of the slope,
a measure of the aspects.
We can create contour lines from the raster data, and
we can begin to do things like modelling, visibility, or
watersheds in drainage networks and all sorts of extreme channels.
Something we'll get to in a later module.
So let's first start talking about how we would calculate the slope for
one of these digital elevation models.
The slopes are calculated locally using a neighborhood function, so
just like we talked about it in the second module where we were dealing with
filtering on raster images, it's relatively close to the same.
We're, essentially, calculating the slope based on the difference in elevation from
one pixel over the distance to all of the other pixels that surround it,
and whatever the maximum is is gonna give us a measure of the maximum slope.
Now, of course, the difference is the distances are different,
whether we're dealing with pixels that are horizontally or
vertically right next to that one versus ones that are kind of diagonally.
So there's gonna be slightly different measures that are used and
this all happens automatically through the tools we're gonna be running.
You're not gonna have to worry about the specifics of how to calculate these.
But just as an example this is what it will look like to find that the maximum
slope for this one central pixel with these other eight around it.
What we're gonna do is simply do the math on it,
find the maximum slope and then that's going to be what's recorded
in that new cell as the slope of that particular cell.
So this is what a slope raster would look like.
With the DEM that's been used to calculate it right next to it.
And you can see pretty clearly that the slopes are sort of scaled from green to
red with green being flatter areas and red being very high slopes.
Crater Lake is one of relatively rare or
few places in the world where the slopes get up almost to 90 degrees, so
these red slopes are actually very, very high, very, very steeply sloped areas.
You can see them around the edge of the crater, around the edge of the lake,
where it's actually becoming the point that it comes up very steeply and
then drops back down.
Another thing that we can calculate that we do frequently from DEM is something
called the aspect and this is essentially the direction that each cell faces.
So, it's the prevailing direction of each cell.
This is very useful for things like solar radiation calculations, things that are to
the south are going to get more sun in the northern hemisphere, or also for erosion.
If you know the directions of the prevailing winds then you know and
idea of what what areas are more likely to have the sediment wind blowing off of them
if there's not vegetation to hold it in place.
And the way that these are calculated are based on degrees, so north is 0 and
then you have all the other degrees coming back around to 360 which is also north.
So calculating one of these, the software does it the same way.
It looks at a central pixel and then it looks at all the ones around it.
Whatever the steepest slope is it then gives it that value of where it's facing.
So you end up with something that looks like this.
Where we have flat things that are kind of unique and there
are not a lot of them in this particular image, but they come in as gray.
Any other slopes that we're seeing,
or any other directions that we're gonna see are going to be colored sort of
with south being red and north being kind of green and gray.
So we end up with these sort of almost trippy looking colored images but
they really do give you a good image or
good idea of what the prevailing directions are.
Now, another thing we can calculate is something called hillshade, and this is,
essentially, given a certain orientation of the sun on a certain elevation of it
above the horizon.
We can use the DEM to calculate areas that are shaded.
So particular times of day or
particular environmental characteristics, times of year.
So there is much more complex calculations that we could use to calculate
the percentage of shade throughout the day or even over an entire year.
And these are really kind of form the basis for calculating solar radiation.
So if you wanted to find a really good spot to put a solar panel,
this is the kind of calculation that you might want to do.
They're also quite useful for
creating kind of a false 3D shading that you can put on to a topographic surface.
Now, the parameters that come in are the azimuth and the altitude.
So the azimuth is essentially the degree from with the sun is pointing and
the altitude is essentially the degree above the horizon that it's facing.
This is what they tend to look like.
They're usually scaled from black which is almost entirely in shadow to high which is
almost entirely in light.
And then we use those,
we can place those transparently over another layer to kind of give it
this false 3D shading like what you see over the aspect raster here on the right.
Now, something else we can calculate is visibility, the DEM can be used to
calculate, to determine what area of land is visible from a particular point or
whether we can see one thing from another thing across the entirety of our image.
This is sort of subsumed into a field that's called viewshed analysis and
basically just a lot of methods for
determining what's visible from any given location on a landscape.
So we might have a central point and then a bunch of lines coming out from it, and
what we can see from this is what is visible and
what isn't colored in different ways.
Now we can also use these topographic surfaces in 3D to sort of drape,
sort of to form the base layer to then drape any aerial photographs or
satellite imagery over top of.
So there are sort of some neat things that we can deal with when we get to the final
module in 3D visualization that we can use these topographic surfaces for.
Now I want to return to talking about where we get terrain data because there
are some different things, there's some different ways to get these in for
particular study areas.
And there are three main ways we can do it.
We can either scan and digitize paper maps, we can vectorize
the contours from these, we can find some pre-made sources of
topographic data from satellites or from the governmental entities.
Or we can work through known elevation points and
do something called a spatial interpolation where we're gonna create
a surface in between the known points that we have.
So topo maps are relatively common,
there's something that we've all probably seen at least once or twice.
There are some idiosyncrasies of the formats that if you're going to
digitize one of these, I encourage you to look into how to read a topo map.
But essentially, once we vectorize, once we digitize
all of the lines that are on there and give them their proper elevations,
we can use that to create an actual digital elevation model out of it.
We can use it as a basis for creating a TIN or a DEM.
This is something that we'll work with little bit in the demonstration for
this module.
Now we can also find sort of pre-built topographic surfaces at varying
resolutions.
One of the bigger ones for the US is what's called the USGS GTOPO30.
And this is at a one kilometer resolution so it's not particularly fine but
it works very well for larger scale areas.
And these are free to download from the USGS Server Explorer.
There is also the shuttle radio topography mission that SRTM,
which is for the US is 30 meter resolution.
This is essentially a shuttle mission where they sent radar down
to at the Earth, measure the topography everywhere.
So for the US this has been processed down to 30 meter resolution.
For the rest of the world it's at 90 meter resolution and
these have been very well processed over the years and they're pretty accurate.
There's also when we talked about the ASTER satellite in the module
on satellite imagery analysis.
I briefly presented that there's two different data recorders on there,
one facing down and one facing back.
And this allows the satellite to create, topographic surfaces.
So you can use, you can create a topographic surface from ASTER data.
And actually, this has been standardized for
the entire globe relatively recently and it's about a 30 meter resolution.
This is the ASTER GDEM.
And the last thing we can do to create a topographic surface is interpolate between
known points.
So this is the process where we would have a series of points with known values and
we're using it to estimate values in between them.
So it's a way from converting point data into a surface data.
So, just as an example, if we wanted to map precipitation.
And we wanted to know what the precipitation was likely to have been
between two different weather stations, we can create
an interpolation based on the values at a bunch of known weather stations and
use that to estimate what it is in between them.
And the exact same thing can be done for topography.
And we do this working with control points,
or points that we have known values that we use to calculate the interpolation.
So this is sort of like the ground control points that we
dealt with when we were dealing with georeferencing in the previous modules.
But in this case, we need to know the actual value at that place, as well.
So we need to know the latitude, the longitude, and the value.
So the basic assumption in most spacial interpolation techniques
is that the value to be estimated at one point is more influenced by closer
by points than by those that are further away.
And this makes a lot of sense,
this is what we call Tobler's first law of geography.
But it really is sort of intuitively makes sense that things that are nearby
are gonna influence that unknown spot more than things that are further away.
So ideally when we're doing an interpolation we have points that
are well distributed across the entire area.
This is not always super common.
Sometimes you have little spots in one place, and less elsewhere.
And there are some mathematical ways to kind of overcome these.
Some of the different interpretation algorithms are better for
less well distributed data than others.
The assumption is that the data we have, the sampling points,
the control points that we have constitute a good sample,
representative sample of the underlying continuous field.
Whether it's elevation, whether it's pollution,
whether it's weather, temperature.
And essentially what we end up doing afterwards is taking an algorithm to
create the surface in between those points.
We will work with this a little in the demonstration for this module as well.
This is what it kind of what it looks like, we have a series of points,
in this case, these are GPS points taken across an area.
We don't know what it looks like in between any given series of points on any
of these sort of white areas.
But we can quite easily interpolate a surface in between them and
then test what that value is likely to be.
Now there are lots of different methods for interpolation.
There are lots of different algorithms that we could use ranging from very,
very basic ones up to ones that are very mathematically complex.
I'm not gonna address the specifics of them in here.
But the ones we're gonna work with mostly during the demonstration are things called
an inverse distance weighted or a spline technique.
And they all kind of lead to generally similar results, but
can have some pretty big differences in data poor area.
So you might wanna determine the accuracy if you're doing this in
a much more intense way using some sort of cross-validation analysis, running
multiple techniques or doing some sort of geo-statistical analysis afterwards.
And there are tools for this in our GIS.
Although, we're not gonna work with them directly here today, and
in the demonstration.
But, I just wanna stress as well,
that any point-based samples can be interpolated to generate a surface.
This is commonly done for the density of artifacts on archaeological sites for
predictive modeling of things for looking at groundwater concentrations.
These are things that are sampled at particular locations and
then interpolated between them.
So it's not just something that's necessarily only for topography.
Now that's a general overview of topography in a GIS context.
Of generating these surfaces, how they work, the types of analysis we might want
to do with them, and when we might want to go a little bit further with our analysis.
Now we're gonna follow this up with two modules that focus on spatial modeling
which is something that oftentimes takes this topographic data and
then combines them into much more complicated series of layer.
That gives us a measure of a particular thing we're trying to analyze.
So the next module we're gonna work with basic spacial modeling and
then we're gonna look at a much more detailed view of this with hydrological
modeling in the one following that.